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  #1  
Old 12-04-2019, 12:29 PM
AndrewLouca AndrewLouca is offline
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Default A New Perspective on Actuarial Science

Hi everyone,

I've been working in P&C for a few years. While taking exams, I noticed that unlike life insurance, there is no standardized mathematical notation; for example, there is no equivalent of tpx. This makes a lot of the material very wordy and imprecise. Because of this, I've made it my goal to create a notation system and use it to write a textbook.

I've finished a draft of the first part of the book, which mathematically explains the need for insurance.

It can be found here: An Introduction to Actuarial Science

I'm not sure what to do with it at this point, but I'm ready to share it, and I'm interested in any feedback that anyone can provide.

Thanks,

Andrew
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  #2  
Old 12-04-2019, 01:02 PM
nonactuarialactuary nonactuarialactuary is offline
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I think I saw something similar on Reddit, and agree with the top comment there that posted a link to the XKCD below.

https://xkcd.com/927/

In theory, it would be nice if common concepts like frequency and severity had consistently defined notation throughout the P&C actuarial world, but getting everyone to adopt the new standards is an enormous uphill battle. A textbook thatís internally consistent is probably the best thing you can realistically expect. For instance, on the Exam 5 syllabus, the Werner/Modlin and Friedland texts replaced dozens of older papers that all used different notation, and thatís generally seen as a good thing. That said, those texts took years to compile, with thousands of dollars spent on external consulting firms employing teams to actuaries to write the texts. It was an extremely significant undertaking to do this for even just the reserving half of the Exam 5 syllabus, so to replicate this for all P&C actuarial concepts is an unrealistically large undertaking without a huge team of staff and a large budget to match. Further, even if you can do all that and write the end-all-be-all textbook for P&C actuarial science, youíve still got to convince people to abandon their own notation and adopt yours. Thatís not easy. Hell, ALAE/ULAE are still common terms in the industry even though financial reporting pushed the industry to adopt the DCCE/AOE split more than 20 years ago. Institutional momentum is a powerful thing.
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  #3  
Old 12-04-2019, 01:13 PM
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Vorian Atreides Vorian Atreides is offline
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Why should there be an "equivalent" of tpx on the P&C side?
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  #4  
Old 12-04-2019, 01:24 PM
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Quote:
Originally Posted by nonactuarialactuary View Post
...Further, even if you can do all that and write the end-all-be-all textbook for P&C actuarial science, youíve still got to convince people to abandon their own notation and adopt yours. Thatís not easy. Hell, ALAE/ULAE are still common terms in the industry even though financial reporting pushed the industry to adopt the DCCE/AOE split more than 20 years ago. Institutional momentum is a powerful thing.
This. I still produce exhibits that say "ALAE" because that's what management expects to see. It's actually DCC, and it has been DCC for 20 years. I don't see any real change of the notation being standardized.

I always tell new employees that the first thing they should do with a data source is verify that they understand what each field actually represents.
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Old 12-04-2019, 01:39 PM
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Definitions are hugely different even within an organization. At my company we just went through a huge effort to rename WP. WP is now the "property" of Finance because it drives statutory reporting. UW now uses "PWP" (Policy written premium) for their definition of WP.

Spoiler:
In case other companies haven't had to deal with this, for a policy effective 12/1/2019, but a $50K change on 2/1/20, UW would bring it back to 2019 because they cared about Policy year writtern premium, whereas Finance put it in 2020.
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  #6  
Old 12-04-2019, 04:38 PM
CuriousGeorge CuriousGeorge is offline
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Quote:
Originally Posted by Vorian Atreides View Post
Why should there be an "equivalent" of tpx on the P&C side?
He's not saying there should be an equivalent calculation, but that we should have a common nomenclature in our work and literature. When a life actuary writes 5p[15]+4 (sorry I didn't bother subscripting properly), nobody has to pore through appendices to interpret what they mean by that. But try to define and reference a cell in a particular triangle, and there are a dozen different conventions.

There is not-insignificant mental effort that you have to expend to internalize a new set of notation for every new paper you read. That's wasteful.

When you want to document a calculation, it is easier for the next person to read it when they don't have to figure out what you meant by C and D, and what your subscripts mean.

Why wouldn't you want a consistent notation where it makes sense?

Last edited by CuriousGeorge; 12-04-2019 at 04:43 PM..
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Old 12-04-2019, 05:22 PM
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Originally Posted by CuriousGeorge View Post
Why wouldn't you want a consistent notation where it makes sense?
I totally agree and have this problem all the time with textbooks and academic papers (hardly an actuarial problem). However, the coordination effort involved to get everyone using the same notation/terminology seems insurmountable. Language consistently defies anyone trying to enforce consistency.

Probably the best you can do is use standard notation across the exams so at least everyone (who has taken these exams) knows one consistent set of notation even if they use different ones in other places.
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Old 12-04-2019, 05:34 PM
Dr T Non-Fan Dr T Non-Fan is offline
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F for Frequency.
S for Severity.

Use subscript or superscript as needed to differentiate among various F's and S's.

That will be 25 cents per book sold, please.
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  #9  
Old 12-04-2019, 07:04 PM
AndrewLouca AndrewLouca is offline
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Quote:
Originally Posted by nonactuarialactuary View Post
I think I saw something similar on Reddit, and agree with the top comment there that posted a link to the XKCD below.

https://xkcd.com/927/

In theory, it would be nice if common concepts like frequency and severity had consistently defined notation throughout the P&C actuarial world, but getting everyone to adopt the new standards is an enormous uphill battle. A textbook thatís internally consistent is probably the best thing you can realistically expect. For instance, on the Exam 5 syllabus, the Werner/Modlin and Friedland texts replaced dozens of older papers that all used different notation, and thatís generally seen as a good thing. That said, those texts took years to compile, with thousands of dollars spent on external consulting firms employing teams to actuaries to write the texts. It was an extremely significant undertaking to do this for even just the reserving half of the Exam 5 syllabus, so to replicate this for all P&C actuarial concepts is an unrealistically large undertaking without a huge team of staff and a large budget to match. Further, even if you can do all that and write the end-all-be-all textbook for P&C actuarial science, youíve still got to convince people to abandon their own notation and adopt yours. Thatís not easy. Hell, ALAE/ULAE are still common terms in the industry even though financial reporting pushed the industry to adopt the DCCE/AOE split more than 20 years ago. Institutional momentum is a powerful thing.
Yea, I made the same post on Reddit.

You're entirely right that getting everyone to adopt a new standard notation will be an enormous uphill battle, but that doesn't mean it's impossible. Also, I think that attempting to create a good notation and trying to get it adopted will be a fun challenge.

Although the chance of getting a new notation adopted widely is low, I think certain things can be done to increase the chances.

The first thing is to make a good notation. At the beginning of my book, I put three quotes that deal with notation, which I'll repeat here.
Quote:
"It is worth noting that notation facilitates discovery. This, in a most wonderful way, reduce's the mind's labour" - Gottfried Leibniz

"We could of course, use any notation we want; do not laugh at notations; invent them, they are powerful. In fact, mathematics is, to a large extent, invention of better notations." - Richard Feynman

"Such is the advantage of a well constructed language that its simplified notation often becomes the source of profound theories" - Pierre-Simon Laplace
So, I think that a good notation should make ideas and concepts easier to understand, and maybe even allow for the discovery of new ideas.

The second thing is to use the notation to write a book. This way, the notation and material can be taught side-by-side. For this to work, the book has to be written well.

For now, these are my aims. I think I've somewhat accomplished them in the first draft I posted. For example, as far as I know (and please correct me if I'm wrong), there currently is no rigorous way of determining the conditions under which it is beneficial or detrimental for different risks to be grouped together. I start to address this question in chapter 5.
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  #10  
Old 12-04-2019, 07:10 PM
AndrewLouca AndrewLouca is offline
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Quote:
Originally Posted by CuriousGeorge View Post
He's not saying there should be an equivalent calculation, but that we should have a common nomenclature in our work and literature. When a life actuary writes 5p[15]+4 (sorry I didn't bother subscripting properly), nobody has to pore through appendices to interpret what they mean by that. But try to define and reference a cell in a particular triangle, and there are a dozen different conventions.

There is not-insignificant mental effort that you have to expend to internalize a new set of notation for every new paper you read. That's wasteful.

When you want to document a calculation, it is easier for the next person to read it when they don't have to figure out what you meant by C and D, and what your subscripts mean.

Why wouldn't you want a consistent notation where it makes sense?
Exactly! That was a great explanation.

This isn't a new idea either. The need for a consistent and standard notation has been addressed in the past.
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